samplemidterm2solutions

# samplemidterm2solutions - Sample Midterm 2, Math 33A, Fall...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Sample Midterm 2, Math 33A, Fall 2007 November 19, 2007 1. (2 pts each) Indicate whether each statement is true or false; you need not show your work here. If T : R n → R n is an invertible linear transformation, B is a basis of R n , and B is the matrix of T with respect to the basis B , then B must be invertible. T F If A is a n by n matrix with exactly one 1 in each row, exactly one 1 in each column, and 0s elsewhere, then det A must be 1 or- 1. T F If A is a n by n matrix, then det 2 A must be equal to 2(det A ). T F If ~v is a vector in R n and W is a subspace of R n , then the length of proj W ~v must be less than or equal to the length of ~v . T F . If W and V are subspaces of R n and W ⊂ V , then it must also be true that W ⊥ ⊂ V ⊥ . T F . Solution. T, T, F, T, F. If T : R n → R n is an invertible linear transformation and A is its matrix with respect to the standard basis, then A is invertible. If S is the change-of-basis matrix for the basis B , then B = S- 1 AS , which is a product of invertible matrices. Hence, which is a product of invertible matrices....
View Full Document

## This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

### Page1 / 3

samplemidterm2solutions - Sample Midterm 2, Math 33A, Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online